Smallest bit prime k tuplet

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k	Smallest 1,000 bit prime k-tuplets	Who ?	When ?	Status ?
1	2⁹⁹⁹ + 1239	Andrey Kulsha	-	Prime
2	2⁹⁹⁹ + 131493 + d, d = 0, 2	Norman Luhn ( PRP / proven primes via PRIMO )	30 Jun 2023	Prime
3	2⁹⁹⁹ + 208538079 + d, d = 0, 2, 6 2⁹⁹⁹ + 81608945 + d, d = 0, 4, 6	Norman Luhn ( PRP / proven primes via PRIMO )	30 Jun 2023	Prime
4	2⁹⁹⁹ + 33899096913 + d, d = 0, 2, 6, 8	Norman Luhn ( PRP / proven primes via PRIMO )	-	Prime
5	2⁹⁹⁹ + 4493853079263 + d, d = 0, 2, 6, 8, 12 2⁹⁹⁹ + 6405588072959 + d, d = 0, 4, 6, 10, 12	Norman Luhn ( PRP / proven primes via PRIMO )	30 Jun 2023	Prime
6	2⁹⁹⁹ + 12373034057705669 + d, d = 0, 4, 6, 10, 12, 16	Norman Luhn ( PRP / proven primes via PRIMO )	03 Jul 2023	Prime

k Smallest 2,000 bit prime k-tuplets Who ? When ? Status ?

1 2¹⁹⁹⁹ + 345 Markus Tervooren ( PRP / proven prime via PRIMO ) 16 Mar 2011 Prime

2 2¹⁹⁹⁹ + 1458003 + d, d = 0, 2 Norman Luhn ( PRP / proven primes via PRIMO ) 01 Jul 2023 Prime

3 2¹⁹⁹⁹ + 354804993 + d, d = 0, 2, 6
2¹⁹⁹⁹ + 1376585669 + d, d = 0, 4, 6 Norman Luhn ( PRP / proven primes via PRIMO ) 01 Jul 2023 Prime

4 2¹⁹⁹⁹ + 253096198293 + d, d = 0, 2, 6, 8 Norman Luhn ( PRP / proven primes via PRIMO ) 02 Jul 2023 Prime

5 2¹⁹⁹⁹ + 665602680629223 + d, d = 0, 2, 6, 8, 12
2¹⁹⁹⁹ + 441836597465189 + d, d = 0, 4, 6, 10, 12 Norman Luhn ( PRP / proven primes via PRIMO ) 20 Jul 2023
21 Jul 2023 Prime

k Smallest 3,000 bit prime k-tuplets Who ? When ? Status ?

1 2²⁹⁹⁹ + 233 Markus Tervooren ( PRP / proven prime via PRIMO ) 16 Aug 2011 Prime

2 2²⁹⁹⁹ + 1792551 + d, d = 0, 2 Norman Luhn ( PRP / proven primes via PRIMO ) 02 Jul 2023 Prime

3 2²⁹⁹⁹ + 2668257093 + d, d = 0, 2, 6
2²⁹⁹⁹ + 6711551075 + d, d = 0, 4, 6 Norman Luhn ( PRP / proven primes via PRIMO ) 03 Jul 2023 Prime

4 2²⁹⁹⁹ + 9156209246163 + d, d = 0, 2, 6, 8 Norman Luhn ( PRP )
Anonymous ( proven primes via PRIMO ) 04 Jul 2023 Prime

5 2²⁹⁹⁹ + 6424729478696073 + d, d = 0, 2, 6, 8, 12
2²⁹⁹⁹ + 7418461178845439 + d, d = 0, 4, 6, 10, 12 Norman Luhn ( PRP / proven primes via PRIMO ) 05 Aug 2023
24 Aug 2023 Prime

k Smallest 4,000 bit prime k-tuplets Who ? When ? Status ?

1 2³⁹⁹⁹ + 311 Markus Tervooren ( PRP / proven prime via PRIMO ) 02 Oct 2011 Prime

2 2³⁹⁹⁹ + 3687783 + d, d = 0, 2 Norman Luhn ( PRP )
Anonymous ( proven primes via PRIMO ) 03 Jul 2023 Prime

3 2³⁹⁹⁹ + 978673449 + d, d = 0, 2, 6
2³⁹⁹⁹ + 2996980565 + d, d = 0, 4, 6 Norman Luhn ( PRP )
Anonymous ( proven primes via PRIMO ) 03 Jul 2023 Prime

4 2³⁹⁹⁹ + 7227471561213 + d, d = 0, 2, 6, 8 Norman Luhn ( PRP / proven primes via PRIMO ) 08 Jul 2023 Prime

k Smallest 5,000 bit prime k-tuplets Who ? When ? Status ?

1 2⁴⁹⁹⁹ + 3843 "Greg" ( proven prime via GP/PARI ) 16 May 2022 Prime

2 2⁴⁹⁹⁹ + 2821251 + d, d = 0, 2 Norman Luhn ( PRP / proven primes via PRIMO ) 03 Jul 2023 Prime

3 2⁴⁹⁹⁹ + 11704701423 + d, d = 0, 2, 6
2⁴⁹⁹⁹ + 13209000695 + d, d = 0, 4, 6 Norman Luhn ( PRP )
Richard G. ( proven primes via GP/PARI )
Anonymous ( proven primes via PRIMO ) 03 Jul 2023 Prime

4 2⁴⁹⁹⁹ + 211512469851123 + d, d = 0, 2, 6, 8 Norman Luhn ( PRP / proven primes via PRIMO ) 17 Jul 2023 Prime

k Smallest 6,000 bit prime k-tuplets Who ? When ? Status ?

1 2⁵⁹⁹⁹ + 4475 Norman Luhn ( PRP / proven prime via PRIMO ) 03 Jul 2023 Prime

2 2⁵⁹⁹⁹ + 28573281 + d, d = 0, 2 Norman Luhn ( PRP / proven primes via PRIMO ) 03 Jul 2023 Prime

3 2⁵⁹⁹⁹ + 2473125783 + d, d = 0, 2, 6
2⁵⁹⁹⁹ + 27748448735 + d, d = 0, 4, 6 Norman Luhn ( PRP )
Richard G. ( proven primes via GP/PARI )
Oliver Kruse ( proven primes via CM ) 03 Jul 2023 Prime

4 2⁵⁹⁹⁹ + 87059009309433 + d, d = 0, 2, 6, 8 Norman Luhn ( PRP / proven primes via PRIMO ) 22 Sep 2023 Prime

k Smallest 7,000 bit prime k-tuplets Who ? When ? Status ?

1 2⁶⁹⁹⁹ + 585 Edwin Hall ( PRP / proven prime via PRIMO ) 05 Mar 2012 Prime

2 2⁶⁹⁹⁹ + 12440451 + d, d = 0, 2 Norman Luhn ( PRP )
Anonymous ( proven primes via PRIMO ) 04 Jul 2023 Prime

3 2⁶⁹⁹⁹ + 3253968573 + d, d = 0, 2, 6
2⁶⁹⁹⁹ + 16729556939 + d, d = 0, 4, 6 Norman Luhn ( PRP )
Oliver Kruse ( proven primes via CM )
Anonymous ( proven primes via PRIMO ) 05 Jul 2023 Prime

4 2⁶⁹⁹⁹ + 99002425776003 + d, d = 0, 2, 6, 8
Norman Luhn ( PRP )
Oliver Kruse ( proven prime via CM ) 28 Sep 2023 Prime

k Smallest 8,000 bit prime k-tuplets Who ? When ? Certificates

1 2⁷⁹⁹⁹ + 2463 Norman Luhn ( PRP )
Oliver Kruse ( proven prime via CM ) 04 Jul 2023 Prime

2 2⁷⁹⁹⁹ + 21178023 + d, d = 0, 2 Norman Luhn ( PRP )
Oliver Kruse ( proven primes via CM ) 04 Jul 2023 Prime

3 2⁷⁹⁹⁹ + 75634774749 + d, d = 0, 2, 6
2⁷⁹⁹⁹ + 47217614525 + d, d = 0, 4, 6 Norman Luhn ( PRP )
Oliver Kruse ( proven primes via CM ) 06 Jul 2023 Prime

k Smallest 9,000 bit prime k-tuplets Who ? When ? Certificates

1 2⁸⁹⁹⁹ + 2039 Norman Luhn ( PRP )
Oliver Kruse ( proven prime via CM ) 04 Jul 2023 Prime

2 2⁸⁹⁹⁹ + 5166819 + d, d = 0, 2 Norman Luhn ( PRP )
Oliver Kruse ( proven primes via CM ) 04 Jul 2023 Prime

3 2⁸⁹⁹⁹ + 14278135689 + d, d = 0, 2, 6
2⁸⁹⁹⁹ + 160079214185 + d, d = 0, 4, 6 Norman Luhn ( PRP )
Oliver Kruse ( proven primes via CM ) 07 Jul 2023 Prime

k	Smallest 2,000 bit prime k-tuplets	Who ?	When ?	Status ?
1	2¹⁹⁹⁹ + 345	Markus Tervooren ( PRP / proven prime via PRIMO )	16 Mar 2011	Prime
2	2¹⁹⁹⁹ + 1458003 + d, d = 0, 2	Norman Luhn ( PRP / proven primes via PRIMO )	01 Jul 2023	Prime
3	2¹⁹⁹⁹ + 354804993 + d, d = 0, 2, 6 2¹⁹⁹⁹ + 1376585669 + d, d = 0, 4, 6	Norman Luhn ( PRP / proven primes via PRIMO )	01 Jul 2023	Prime
4	2¹⁹⁹⁹ + 253096198293 + d, d = 0, 2, 6, 8	Norman Luhn ( PRP / proven primes via PRIMO )	02 Jul 2023	Prime
5	2¹⁹⁹⁹ + 665602680629223 + d, d = 0, 2, 6, 8, 12 2¹⁹⁹⁹ + 441836597465189 + d, d = 0, 4, 6, 10, 12	Norman Luhn ( PRP / proven primes via PRIMO )	20 Jul 2023 21 Jul 2023	Prime

k	Smallest 3,000 bit prime k-tuplets	Who ?	When ?	Status ?
1	2²⁹⁹⁹ + 233	Markus Tervooren ( PRP / proven prime via PRIMO )	16 Aug 2011	Prime
2	2²⁹⁹⁹ + 1792551 + d, d = 0, 2	Norman Luhn ( PRP / proven primes via PRIMO )	02 Jul 2023	Prime
3	2²⁹⁹⁹ + 2668257093 + d, d = 0, 2, 6 2²⁹⁹⁹ + 6711551075 + d, d = 0, 4, 6	Norman Luhn ( PRP / proven primes via PRIMO )	03 Jul 2023	Prime
4	2²⁹⁹⁹ + 9156209246163 + d, d = 0, 2, 6, 8	Norman Luhn ( PRP ) Anonymous ( proven primes via PRIMO )	04 Jul 2023	Prime
5	2²⁹⁹⁹ + 6424729478696073 + d, d = 0, 2, 6, 8, 12 2²⁹⁹⁹ + 7418461178845439 + d, d = 0, 4, 6, 10, 12	Norman Luhn ( PRP / proven primes via PRIMO )	05 Aug 2023 24 Aug 2023	Prime

k	Smallest 4,000 bit prime k-tuplets	Who ?	When ?	Status ?
1	2³⁹⁹⁹ + 311	Markus Tervooren ( PRP / proven prime via PRIMO )	02 Oct 2011	Prime
2	2³⁹⁹⁹ + 3687783 + d, d = 0, 2	Norman Luhn ( PRP ) Anonymous ( proven primes via PRIMO )	03 Jul 2023	Prime
3	2³⁹⁹⁹ + 978673449 + d, d = 0, 2, 6 2³⁹⁹⁹ + 2996980565 + d, d = 0, 4, 6	Norman Luhn ( PRP ) Anonymous ( proven primes via PRIMO )	03 Jul 2023	Prime
4	2³⁹⁹⁹ + 7227471561213 + d, d = 0, 2, 6, 8	Norman Luhn ( PRP / proven primes via PRIMO )	08 Jul 2023	Prime

k	Smallest 5,000 bit prime k-tuplets	Who ?	When ?	Status ?
1	2⁴⁹⁹⁹ + 3843	"Greg" ( proven prime via GP/PARI )	16 May 2022	Prime
2	2⁴⁹⁹⁹ + 2821251 + d, d = 0, 2	Norman Luhn ( PRP / proven primes via PRIMO )	03 Jul 2023	Prime
3	2⁴⁹⁹⁹ + 11704701423 + d, d = 0, 2, 6 2⁴⁹⁹⁹ + 13209000695 + d, d = 0, 4, 6	Norman Luhn ( PRP ) Richard G. ( proven primes via GP/PARI ) Anonymous ( proven primes via PRIMO )	03 Jul 2023	Prime
4	2⁴⁹⁹⁹ + 211512469851123 + d, d = 0, 2, 6, 8	Norman Luhn ( PRP / proven primes via PRIMO )	17 Jul 2023	Prime

k	Smallest 6,000 bit prime k-tuplets	Who ?	When ?	Status ?
1	2⁵⁹⁹⁹ + 4475	Norman Luhn ( PRP / proven prime via PRIMO )	03 Jul 2023	Prime
2	2⁵⁹⁹⁹ + 28573281 + d, d = 0, 2	Norman Luhn ( PRP / proven primes via PRIMO )	03 Jul 2023	Prime
3	2⁵⁹⁹⁹ + 2473125783 + d, d = 0, 2, 6 2⁵⁹⁹⁹ + 27748448735 + d, d = 0, 4, 6	Norman Luhn ( PRP ) Richard G. ( proven primes via GP/PARI ) Oliver Kruse ( proven primes via CM )	03 Jul 2023	Prime
4	2⁵⁹⁹⁹ + 87059009309433 + d, d = 0, 2, 6, 8	Norman Luhn ( PRP / proven primes via PRIMO )	22 Sep 2023	Prime

k	Smallest 7,000 bit prime k-tuplets	Who ?	When ?	Status ?
1	2⁶⁹⁹⁹ + 585	Edwin Hall ( PRP / proven prime via PRIMO )	05 Mar 2012	Prime
2	2⁶⁹⁹⁹ + 12440451 + d, d = 0, 2	Norman Luhn ( PRP ) Anonymous ( proven primes via PRIMO )	04 Jul 2023	Prime
3	2⁶⁹⁹⁹ + 3253968573 + d, d = 0, 2, 6 2⁶⁹⁹⁹ + 16729556939 + d, d = 0, 4, 6	Norman Luhn ( PRP ) Oliver Kruse ( proven primes via CM ) Anonymous ( proven primes via PRIMO )	05 Jul 2023	Prime
4	2⁶⁹⁹⁹ + 99002425776003 + d, d = 0, 2, 6, 8	Norman Luhn ( PRP ) Oliver Kruse ( proven prime via CM )	28 Sep 2023	Prime

k	Smallest 8,000 bit prime k-tuplets	Who ?	When ?	Certificates
1	2⁷⁹⁹⁹ + 2463	Norman Luhn ( PRP ) Oliver Kruse ( proven prime via CM )	04 Jul 2023	Prime
2	2⁷⁹⁹⁹ + 21178023 + d, d = 0, 2	Norman Luhn ( PRP ) Oliver Kruse ( proven primes via CM )	04 Jul 2023	Prime
3	2⁷⁹⁹⁹ + 75634774749 + d, d = 0, 2, 6 2⁷⁹⁹⁹ + 47217614525 + d, d = 0, 4, 6	Norman Luhn ( PRP ) Oliver Kruse ( proven primes via CM )	06 Jul 2023	Prime

k	Smallest 9,000 bit prime k-tuplets	Who ?	When ?	Certificates
1	2⁸⁹⁹⁹ + 2039	Norman Luhn ( PRP ) Oliver Kruse ( proven prime via CM )	04 Jul 2023	Prime
2	2⁸⁹⁹⁹ + 5166819 + d, d = 0, 2	Norman Luhn ( PRP ) Oliver Kruse ( proven primes via CM )	04 Jul 2023	Prime
3	2⁸⁹⁹⁹ + 14278135689 + d, d = 0, 2, 6 2⁸⁹⁹⁹ + 160079214185 + d, d = 0, 4, 6	Norman Luhn ( PRP ) Oliver Kruse ( proven primes via CM )	07 Jul 2023	Prime